Question

$\sin( \frac{x}{4} ) + \cos( \frac{x}{2} ) = 1$

Answer 1

sin(x/4)+cos(2·x/4)=1
sin(x/4)+cos²(x/4)-sin²(x/4)=1
sin(x/4)+1-sin²(x/4)-sin²(x/4)=1
-2sin²(x/4)+sin(x/4)=0
-2sin(x/4)(sin(x/4)-1)=0
sin(x/4)=0 sau sin(x/4)=1
x/4=0+kπ  sau x/4=π/2+2nπ
x=4kπ,k∈Z sau x=2π+8nπ,n∈Z